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%I A105871 #11 Jan 23 2023 11:39:54
%S A105871 1,2,6,22,85,336,1350,5492,22554,93300,388201,1622868,6811056,
%T A105871 28680356,121111440,512684484,2174928031,9243973062,39354962345,
%U A105871 167799259130,716414975613,3062437147352,13105366936465,56139506687280
%N A105871 a(n) = sum{k=0..floor(n/2), C(2*n-3*k, n)*C(n-k, k)}
%F A105871 a(n) = sum{k=0..floor(n/2), C(2*n-3*k, n)*C(n-k, k)}
%F A105871 Conjecture: 5*n*(n-1)*(3*n-10)*a(n) -3*(n-1)*(21*n^2-63*n-20)*a(n-1) +3*(-3*n^3+107*n^2-446*n+444)*a(n-2) +(3*n^3-259*n^2+1279*n-1575)*a(n-3) +3*(-21*n^3+210*n^2-673*n+694)*a(n-4) -3*(n-3)*(3*n^2-8*n-7)*a(n-5) -2*(n-4)*(3*n-7)*(2*n-9)*a(n-6)=0. - _R. J. Mathar_, Feb 20 2015
%p A105871 A105871 := proc(n)
%p A105871     add(binomial(2*n-3*k, n)*binomial(n-k, k),k=0..floor(n/2)) ;
%p A105871 end proc: # _R. J. Mathar_, Feb 20 2015
%t A105871 Table[Sum[Binomial[2n-3k,n]Binomial[n-k,k],{k,0,Floor[n/2]}],{n,0,30}] (* _Harvey P. Dale_, Jan 23 2023 *)
%o A105871 (PARI) a(n)=sum(k=0,floor(n/2), binomial(2*n-3*k, n)*binomial(n-k, k) ); /* _Joerg Arndt_, Mar 06 2013 */
%K A105871 easy,nonn
%O A105871 0,2
%A A105871 _Paul Barry_, Apr 23 2005

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